### Wave Digital Filters

The idea of wave digital filters is to digitize RLC circuits (and certain more general systems) as follows:

- Determine the ODEs describing the system (PDEs also workable).
- Express all physical quantities (such as force and velocity) in
terms of
*traveling-wave components*. The traveling wave components are called*wave variables*. For example, the force on a mass is decomposed as , where is regarded as a traveling wave propagating*toward*the mass, while is seen as the traveling component propagating*away from*the mass. A ``traveling wave'' view of force mediation (at the speed of light) is actually much closer to underlying physical reality than any instantaneous model. - Next, digitize the resulting traveling-wave system using the
*bilinear transform*(§7.3.2,[449, p. 386]). The bilinear transform is equivalent in the time domain to the*trapezoidal rule for numerical integration*(§7.3.2). - Connect elementary units together by means of
*-port scattering junctions*. There are two basic types of scattering junction, one for parallel, and one for series connection. The theory of scattering junctions is introduced in the*digital waveguide*context (§C.8).

We will not make much use of WDFs in this book, preferring instead more prosaic finite-difference models for simplicity. However, we will utilize closely related concepts in the digital waveguide modeling context (Chapter 6).

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